Environmental Engineering Reference
In-Depth Information
Chapter 5
FREQUENCY COMPENSATION TECHNIQUES
In the previous chapter we demonstrated the necessity, in a feedback
network, to achieve an open loop dominant-pole frequency response whose a
phase margin is greater than 45° (or
K >
1). Indeed, this condition not only
ensures closed-loop stability but also avoids unacceptably underdamped
closed-loop responses. Unfortunately, many amplifiers, and particularly
broadbanded amplifiers, earmarked for use as open-loop cells are not
characterised by dominant-pole frequency responses. The loop-gain
frequency response of these amplifiers must be therefore properly optimised
in accordance with standard design practices known as
frequency
compensation techniques
[SS91], [GM93], [LS94]. These methods imply the
inclusion of compensation
RC
networks in the uncompensated circuit to
introduce additional poles or to modify the original loop-gain poles so as to
provide a given phase margin.
Referring to Fig. 4.8, it is easily understood that the simplest way to
achieve stability is to reduce the loop gain. If the frequency of the poles
remain unchanged, the unity-gain frequency is decreased by the same
amount as the loop gain reduction and consequently the ratio between the
second pole and the gain-bandwidth product is increased. The loop gain can
be reduced via the feedback factor
f
or by decreasing the amplifier open-loop
gain. However, neither are practical design choices because changing the
loop gain may conflict with closed-loop performance such as gain, accuracy,
etc. Moreover, it is worthwhile noting that compensation must be ensured for
all the possible feedback configurations. If the feedback factor is not
specified, compensation should be performed in the worst-case condition,
that corresponds to the unitary feedback (i.e., with the highest loop gain and
gain-bandwidth product,
f =
1 and
